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On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues

- Gábor Pataki
- Math. Oper. Res.
- 1998

We derive some basic results on the geometry of semidefinite programming (SDP) and eigenvalue-optimization, i.e., the minimization of the sum of the k largest eigenvalues of a smooth matrix-valued… (More)

- Gábor Pataki
- 2000

Consider the primal-dual pair of optimization problems
$$ \begin{gathered} Min \left\langle {c,x} \right\rangle {\rm M}ax \left\langle {b,y} \right\rangle \hfill \\ (P) s.t. x \in K s.t. z \in K*… (More)

The active field of Functional Data Analysis (about understanding the variation in a set of curves) has been recently extended to Object Oriented Data Analysis, which considers populations of more… (More)

- Gábor Pataki
- 2013

The facial reduction algorithm (FRA) of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program
$$\displaystyle{ \sup \,\{\,\langle c,x\rangle… (More)

- Gábor Pataki
- Math. Oper. Res.
- 2007

When is the linear image of a closed convex cone closed? We present very simple and intuitive necessary conditions that (1) unify, and generalize seemingly disparate, classical sufficientconditions… (More)

- E. Andrew Balas, Sebastián Ceria, Gérard Cornuéjols, Gábor Pataki
- Cliques, Coloring, and Satisfiability
- 1993

Abstract : This paper presents an integer programming approach to the maximum clique problem. An initial linear programming relaxation is solved and, when there is an integrality gap, this relaxation… (More)

- Gábor Pataki
- SIAM Review
- 2003

We designed a simple computational exercise to compare weak and strong integer programming formulations of the traveling salesman problem. Using commercial IP software, and a short (60 line long)… (More)

- Gábor Pataki, Levent Tunçel
- Math. Program.
- 2001

Abstract.We prove that strict complementarity, primal and dual nondegeneracy of optimal solutions of convex optimization problems in conic form are generic properties. In this paper, we say generic… (More)

- Minghui Liu, Gábor Pataki
- Math. Program.
- 2015

In conic linear programming—in contrast to linear programming—the Lagrange dual is not an exact dual: it may not attain its optimal value, or there may be a positive duality gap. The corresponding… (More)